A university dean is interested in determining the proportion of students who receive some sort of financial aid.Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.The 95% confidence interval for Interpret this interval.
A)We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.
B)95% of the students get between 52% and 66% of their tuition paid for by financial aid.
C)We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid.
D)We are 95% confident that 59% of the students are on some sort of financial aid.

Question

A university dean is interested in determining the proportion of students who receive some sort of financial aid.Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.The 95% confidence interval for  Interpret this interval.
A)We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66. 
B)95% of the students get between 52% and 66% of their tuition paid for by financial aid. 
C)We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid. 
D)We are 95% confident that 59% of the students are on some sort of financial aid.

Quizplus · Accepted Answer

The confidence interval is calculated for the proportion of all students receiving financial aid. The interval is (0.52, 0.66) and we are 95% confident that the true proportion falls within this range. The confidence interval provides a range of possible values for the true proportion of students receiving financial aid. The statement "we are 95% confident" means that if we were to repeat this sampling process many times, 95% of the resulting confidence intervals would contain the true proportion. Therefore, the correct interpretation is that we are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.

A University Dean Is Interested in Determining the Proportion of Students